3.2.4"doublecheck"

This teachpack defines automated random test generation as a complement to
theorem proving. Each property declared via DoubleCheck is tested randomly by
Dracula, and verified logically by ACL2.

3.2.4.1Properties

(defpropertyname(bind...)test)

bind

=

(varhypmaybe-value)

maybe-value

=

|

:valuerandom-expr

(check-properties)

Use defproperty to define DoubleCheck tests in a file, then call
check-properties at the end to display the results. This opens a GUI
in DrScheme (but renders test results as text in this documentation).

Each defproperty form defines a property called name which
states that test must be true for all assignments to free variables,
much like defthm. The binding clauses declare the free variables and
constrain their values with hypotheses, much like the common use of
implies in theorems.

When properties are run in Dracula, it generates random values for the variables
during each trial. The hypotheses are used to constrain these values. The user
may declare the random distribution used for each variable with a
:value clause, or leave it to the default distribution of ACL2 values.

When properties are run in ACL2, they are equivalent to a theorem with
hypotheses expressed using implies. Any random distributions, if
supplied, are ignored.

Example:

; Prove that reverse is its own inverse:

(defthmreverse-reverse-theorem

(implies(true-listplst)

(equal(reverse(reverselst))lst)))

; Now test the same thing with DoubleCheck:

(defpropertyreverse-reverse-property

((lst(true-listplst)))

(equal(reverse(reverselst))lst))

; Run the tests:

(check-properties)

3.2.4.2Random Distributions

Randomness is an inherently imperative process. As such, it is not reflected in
the logic of ACL2. The random distribution functions of DoubleCheck may only be
used within :value clauses of defproperty, or in other random
distributions.

(random-sexp)→t

(random-atom)→atom

(random-boolean)→booleanp

(random-symbol)→symbolp

(random-char)→characterp

(random-string)→stringp

(random-number)→acl2-numberp

(random-rational)→rationalp

(random-integer)→integerp

(random-natural)→natp

These distributions produce random elements of the builtin Dracula types. When
no distribution is given for a property binding, defproperty uses
random-sexp by default.

(random-betweenlohi)→integerp

lo:integerp

hi:integerp

Produces an integer uniformly distributed between lo and hi,
inclusive; lo must be less than or equal to hi.

(random-data-size)→natp

Produces a natural number weighted to prefer small numbers, appropriate for
limiting the size of randomly produced values. This is the default distribution
for the length of random lists and the size of random s-expressions.

(random-element-oflst)→t

lst:proper-consp

Chooses among the elements of lst, distributed uniformly.

(random-list-ofexprmaybe-size)

maybe-size

=

|

:sizesize

Constructs a random list of length size (default
(random-data-size)), each of whose elements is the result of evaluating
expr.

(random-sexp-ofexprmaybe-size)

maybe-size

=

|

:sizesize

Constructs a random cons-tree with size total
cons-pairs (default (random-data-size)), each of whose leaves
is the result of evaluating expr.

(defrandomname(arg...)body)

The defrandom form defines new random distributions. It takes the same
form as defun, but the body may refer to other random distributions.

Example:

; Construct a distribution for random association lists:

(defrandomrandom-alist(len)

(random-list-of(cons(random-atom)(random-sexp)):sizelen))

; ...and now use it:

(defpropertyacons-preserves-alistp

((alist(alistpalist):value(random-alist(random-between010)))

(key(atomkey):value(random-atom))

(datumt))

(alistp(aconskeydatumalist)))

(random-caseclause...)

clause

=

expr

|

expr:weightweight

Chooses an expression from the clauses, each with the associated weight
(defaulting to 1), and yields its result; the other expressions are not
evaluated. This is useful with defrandom for defining recursive
distributions.

Be careful of the branching factor; a distribution with a high probability of
unbounded recursion is often unlikely to terminate. It is useful to give a
depth parameter to limit recursion.